**Number Puzzle #67**

4+5+4+5 => 18 => 1+8 => 9 => square of 9 => 81

5+6+5+6 => 22 => 2+2 => 4 => square of 4 => 16

6+7+6+7 => 26 => 2+6 => 8 => square of 8 => 64

Thus the patter is sum of the digits till we get single digit and then square of the the single digit.

**Method 1:**

So lets assume the missing number is x

thus 1+2+1+x = x + 4

Now if x is less then or equal to 5(i.e. x+4 is single digit)

(x+4)(x+4) = 16 =>** x = 0**

Now if x is greater then 5( i.e. x + 4 is two digit number)

lets replace x by 6+y (where y is single digit)

x+4 => 6+y+4 => 10 + y => y +1 => (y+1)*(y+1) = 16 => y = 3

**thus x = 6+y = 9.**

**Note:** If we assume missing number can be more then single digit.

**Method 2:**

its the reverse engineering method => to get 16 the sum of digits should be 4

we already have 1+2+1 = 4 thus missing number can be 0

other ways to get the sum of digits as 4 => 13, i.e. missing number = 13-4 = 9

other ways is 22, i.e. missing number 22-4 = 18

other way is 31, i.e. missing number 31 – 4 = 27

other way is 40, thus missing number 40 -4 = 36

so there can be more such numbers

Laxmi Alagia says

Ans is 2